I've had problems with my router before, usually mine gets too hot. It might also be the type of traffic going through it..when I used to run bittorrent a lot, downloading/uploading a ton of torrents, my network went down about one every few days..and I had to unplug my router and plug it back in.

You could try replacing the router and see if that fixes it.

Check to see if your networked computers can still talk to each other when the internet goes down. If they can, it's probably your modem. If they can't talk, it is probably your router.